Is there only one way to divide an equilateral triangle into congruent fourths?

Question

Suppose we wish to divide an equilateral triangle into fourths, such that each piece is congruent. (Let's also require connectedness.) One way to do this is to connect the medians, forming one inverted triangle in the center and three at the corners. Is this the only way? Are there any other ways to divide an equilateral triangle into congruent fourths?

Answer 1

Depending on how strict you are with your notion of connectedness, here are four congruent sets whose closures are connected and whose interiors are disjoint: